A clock with a metallic pendulum gains `6` seconds each day when the temperature is `20^(@)C` and loses `6` second when the temperature is `40^(@)C`. Find the coefficient of linear expansions of the metal.

Options

A. `1.4xx10^(-5) "^(@)C^(-1)`
B. `1.4xx10^(-6) "^(@)C^(-1)`
C. `1.4xx10^(-4) "^(@)C^(-1)`
D. `1.4xx10^(-6) "^(@)C^(-1)`

Answer

A

Explanation

For simply pendulum `T=2pi`
`sqrt((l)/(g)) implies T alpha l^(1//2) implies (DeltaT)/(T) = (1)/(2) (Deltal)/(l) = (1)/(2) alphaDeltatheta`
Assuming clock gives correct time at temperature